On the implausibility of constant-round public-coin zero-knowledge proofs

Yi Deng*, Juan Garay, San Ling, Huaxiong Wang, Moti Yung

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Citations (Scopus)

Abstract

We consider the problem of whether there exist non-trivial constant-round public-coin zero-knowledge (ZK) proofs. To date, in spite of high interest in the problem, there is no definite answer to the question. We focus on the type of ZK proofs that admit a universal simulator (which handles all malicious verifiers), and show a connection between the existence of such proof systems and a seemingly unrelated “program functionality distinguishing” problem: For a natural class of constant-round public-coin ZK proofs (which we call “canonical,” since all known ZK protocols fall into this category), a session prefix output by the universal simulator can actually be used to distinguish a non-trivial property of the next-step functionality of the verifier’s code. Our result can be viewed as new evidence against the existence of constant-round public-coin ZK proofs, since the existence of such a proof system will bring about either one of the following: (1) a positive result for the above functionality-distinguishing problem, a typical goal in reverse-engineering attempts, commonly believed to be notoriously hard, or (2) a major paradigm shift in simulation strategies, beyond the only known (straight-line simulation) technique applicable to their argument counterpart, as we also argue. Note that the earlier negative evidence on constant-round public-coin ZK proofs is Barack, Lindell and Vadhan [FOCS 2003]’s result, which was based on the incomparable assumption of the existence of certain entropy-preserving hash functions, now known not to be achievable from standard assumptions via black-box reduction. The core of our technical contribution is showing that there exists a single verifier step for constant-round public-coin ZK proofs whose functionality (rather than its code) is crucial for a successful simulation. This is proved by combining a careful analysis of the behavior of a set of verifiers in the above protocols and during simulation, with an improved structure-preserving version of the well-known Babai-Moran Speedup (de-randomization) Theorem, a key tool of independent interest.

Original languageEnglish
Title of host publicationSecurity and cryptography for networks
Subtitle of host publication10th International Conference, SCN 2016, Amalfi, Italy, August 31-September 2, 2016, Proceedings
EditorsVassilis Zikas, Roberto De Prisco
Place of PublicationCham, Switzerland
PublisherSpringer, Springer Nature
Chapter13
Pages237-253
Number of pages17
ISBN (Electronic)9783319446189
ISBN (Print)9783319446172
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event10th International Conference on Security and Cryptography for Networks, SCN 2016 - Amalfi, Italy
Duration: 31 Aug 20162 Sep 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9841
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other10th International Conference on Security and Cryptography for Networks, SCN 2016
CountryItaly
CityAmalfi
Period31/08/162/09/16

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